M + Ng potential energy curves including spin-orbit coupling for M = K, Rb, Cs and Ng = He, Ne, Ar

Spectroscopy of Alkali Atoms in Solid Matrices of Rare Gases: Experimental Results and Theoretical Analysis

We present an experimental and theoretical investigation of the spectroscopy of dilute alkali atoms in a solid matrix of inert gases at cryogenic temperatures, specifically Rubidium atoms in a solid Argon or Neon matrix, and related aspects of the interaction energies between the alkali atoms and the atoms of the solid matrix. The system considered is relevant for matrix isolation spectroscopy, and it is at the basis of a recently proposed detector of cosmological axions, exploiting magnetic-type transitions between Zeeman sublevels of alkali atoms in a magnetic field, tuned to the axion mass, assumed in the meV range. Axions are one of the supposed constituents of the dark matter (DM) of the Universe. This kind of spectroscopy could be also relevant for the experimental search of new physics beyond the Standard Model, in particular the search of violations of time-reversal or parity-charge-conjugation (CP) symmetry. In order to efficiently resolve the axion-induced transition in alkali-doped solid matrices, it is necessary to reduce as much as possible the spectral linewidth of the electronic transitions involved. The theoretical investigation presented in this paper aims to estimate the order of magnitude of the inhomogeneous contribution to the linewidth due to the alkali–matrix interactions (Coulomb/exchange and dispersion), and to compare the theoretical results with our experimental measurements of spectra of dilute Rubidium atoms in Argon and Neon solid matrix. The comparison of the expected or measured spectral linewidths will be important for selecting the most appropriate combination of alkali atoms and matrix inert elements to be used in the proposed axion detection scheme. It is finally suggested that dilute Lithium atoms diffused in a cold parahydrogen solid matrix could be, overall, a good system upon which the proposed detector could be based.

Noble-gas atoms characterized by hyperfine frequency shift of lithium atom

We report an experimental and theoretical study on the shift of the hyperfine splitting frequency of ground-state Li atoms in noble gases, He, Ne, Ar, and Xe. The frequency shift is due to the change in the electron-spin density at the Li nuclei induced by collisions to the noble-gas atoms. The electron density is calculated along the interatomic distance in a pseudopotential and a dispersion potential. Based on the measured and the calculated frequency shifts, we find the importance of attractive force in collisions to helium as well as heavy noble-gas atoms. Taking advantage of the simple energy structure of the Li atom, we obtain the s wave scattering length for free electrons on noble-gas atoms by using the hyperfine splitting frequency as a precise measure.

Enhanced Coupling of Electron and Nuclear Spins by Quantum Tunneling Resonances

Noble-gas spins feature hours-long coherence times, owing to their great isolation from the environment, and find practical usage in various applications. However, this isolation leads to extremely slow preparation times, relying on weak spin transfer from an electron-spin ensemble. Here we propose a controllable mechanism to enhance this transfer rate. We analyze the spin dynamics of helium-3 atoms with hot, optically excited potassium atoms and reveal the formation of quasibound states in resonant binary collisions. We find a resonant enhancement of the spin-exchange cross section by up to 6 orders of magnitude and 2 orders of magnitude enhancement for the thermally averaged, polarization rate coefficient. We further examine the effect for various other noble gases and find that the enhancement is universal. We outline feasible conditions under which the enhancement may be experimentally observed and practically utilized.

Solvation of Isoelectronic Halide and Alkali Metal Ions by Argon Atoms

This work systematically examines the interactions of alkali metal cations and their isoelectronic halide counterparts with up to six solvating Ar atoms (M⁺Ar_n and X^-Ar_n, where M = Li, Na, K, and Rb; X = H, F, Cl, and Br; and n = 1-6) via full geometry optimizations with the MP2 method and robust, correlation-consistent quadruple-ζ (QZ) basis sets. 116 unique M⁺Ar_n and X^-Ar_n stationary points have been characterized on the MP2/QZ potential energy surface. To the best of our knowledge, approximately two dozen of these stationary points have been reported here for the first time. Some of these new structures are either the lowest-energy stationary point for a particular cluster or energetically competitive with it. The CCSD(T) method was employed to perform additional single-point energy computations upon all MP2/QZ-optimized structures using the same basis set. CCSD(T)/QZ results indicate that internally solvated structures with the ion at/near the geometric center of the cluster have appreciably higher energies than those placing the ion on the periphery. While this study extends the prior investigations of M⁺Ar_n clusters found within the literature, it notably provides one of the first thorough characterizations of and comparisons to the corresponding negatively charged X^-Ar_n clusters.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. I. Formalism

Analytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to at least 3n + 1 calculations for finite difference methods, where n is the number of nuclei. Analytic nonadiabatic derivative coupling terms (DCTs), which are calculated in a similar fashion, are used to remove nondiagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation, i.e., that assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities, gradients and DCTs, for the State-Averaged MultiReference Configuration Interaction with Singles and Doubles (MRCI-SD) wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. Calculation of these terms is critical in successfully modeling the dynamics of systems that depend on transitions between potential energy surfaces split by the spin-orbit operator, such as diode-pumped alkali lasers. A formalism for calculating the transition density matrices and analytic derivative coupling terms for such systems is presented.

Analytic non-adiabatic derivative coupling terms for spin-orbit MRCI wavefunctions. II. Derivative coupling terms and coupling angle for KHeA2Π1/2⇔KHeB2Σ1/2

A method for calculating the analytic nonadiabatic derivative coupling terms (DCTs) for spin-orbit multi-reference configuration interaction wavefunctions is reviewed. The results of a sample calculation using a Stuttgart basis for KHe are presented. Additionally, the DCTs are compared with a simple calculation based on the Nikitin's 3 × 3 description of the coupling between the Σ and Π surfaces, as well as a method based on Werner's analysis of configuration interaction coefficients. The nonadiabatic coupling angle calculated by integrating the radial analytic DCTs using these different techniques matches extremely well. The resultant nonadiabatic energy surfaces for KHe are presented.

Excited interatomic potential energy surfaces of Rb + He that correlate with Rb terms 52S through 72S

The excited state interatomic potential energy surfaces for Rb + He are computed at the spin-orbit multi-reference configuration interaction level of theory using all-electron basis sets of triple and quadruple-zeta quality that have been contracted for Douglas-Kroll-Hess (DKH) Hamiltonian and includes core-valence correlation. Davidson-Silver corrections (MRCI+Q) are employed to ameliorate size consistency error. An extrapolation of CASSCF energies is performed using the procedure of Karton and Martin whereas extrapolation of correlation energy is performed using an expression involving the inverse powers of (lmax + 1/2), the highest angular momentum value present in the basis set. The spin-orbit energies in the limit of complete basis set are obtained by replacing the energy eigenvalues in the spin-orbit matrix by the relativistic-corrected MRCI+Q energies extrapolated to the complete basis set limit. MRCI diabatic potential energy surfaces for a few selected 2Σ states are calculated to study the general topology and avoided crossings and repulsive form of the 6s 2Σ+ state. Important features of the potential energy surfaces are discussed with implications for alkali laser spectroscopy.

Ab initio interatomic potentials and transport properties of alkali metal (M = Rb and Cs)-rare gas (Rg = He, Ne, Ar, Kr, and Xe) media

We performed a first principle systematic calculation on the adiabatic potential energy curves (PECs) of alkali metal (M = Rb and Cs) - rare gas (Rg = He, Ne, Ar, Kr, and Xe) van der Waals molecules over a wide range of interatomic distance R. All electron basis sets of triple and quadruple zeta valence quality were used for the He, Ne, Ar and Kr atoms. Scalar relativistic effects were taken into account for the heavy Rb, Cs and Xe atoms by means of Dirac-Fock effective core potentials. The correlated ground state energies have been obtained within the framework of the spin unrestricted open-shell coupled cluster method, with perturbative treatment of triple excitations. The electronic energies were corrected for the basis set superposition error (BSSE) using the counterpoise method. Energies were extrapolated to the complete basis set (CBS) limit using a two-point scheme. The energy convergence towards the CBS limit was monitored by the saturation of the dummy atom basis set that included bond functions centered at the midpoint of the interatomic distance. The ab initio point-wise PEC was followed to small R to the point where the energy was 0.5 Hartree above the dissociation limit. A Morse long-range (MLR, UM Rg(R)) potential possessing the correct asymptotic behavior at R → ∞ was fitted to the single point energies. The resulting set of fully analytical MLR potentials was then used to evaluate classical collision integrals over a wide range of collision energies. By this means, diffusion coefficients (DM Rg(T)) were predicted as functions of the translation temperature T ≤ 3000 K. The reliability of the present ab initio UM Rg(R) and DM Rg(T) functions was accessed through a comparison with previous theoretical and experimental results.

Theoretical Cross Sections of the Inelastic Fine Structure Transition M(2P1/2) + Ng ↔ M(2P3/2) + Ng for M = K, Rb, and Cs and Ng = He, Ne, and Ar

Scattering matrix elements of the inelastic fine structure transition M(²P_1/2) + Ng ↔ M(²P_3/2) + Ng are computed using the channel packet method (CPM) for alkali-metal atoms M = K, Rb, and Cs, as they collide with noble-gas atoms Ng = He, Ne, and Ar. The calculations are performed within the block Born-Oppenheimer approximation where excited state V_A²Π1/2(R), V_A²Π3/2(R), and V_B²Σ1/2(R) adiabatic potential energy surfaces are used together with a Hund's case (c) basis to construct a 6 × 6 diabatic representation of the electronic Hamiltonian. Matrix elements of the angular kinetic energy of the nuclei incorporate Coriolis coupling and, together with the diabatic representation of the electronic Hamiltonian, yield a 6 × 6 effective potential energy matrix. This matrix is diagonal in the asymptotic limit of large internuclear separation with eigenvalues that correlate to the ²P_j alkali atomic energy levels. Scattering matrix elements are computed using the CPM by preparing reactant and product wave packets on the effective potential energy surfaces that correspond to the excited ²P_j alkali states of interest. The reactant wave packet is then propagated forward in time using the split operator method together with a unitary transformation between the adiabatic and diabatic representations. The Fourier transformation of the correlation function between the evolving reactant wave packet and stationary product wave packet yields state-to-state scattering matrix elements as a function of energy for a particular choice of total angular momentum J. Calculations are performed for energies that range from 0.0 to 0.01 hartree and values of J that start with a minimum of J = 0.5 for all M + Ng pairs up to a maximum that ranges from J = 450.5 for KAr to J = 100.5 for CsAr. A sum over J together with an average over energy is used to compute thermally averaged cross sections for a temperature range of T = 0-400 K.

Phase-modulated electronic wave packet interferometry reveals high resolution spectra of free Rb atoms and Rb*He molecules

Phase-modulated wave packet interferometry is combined with mass-resolved photoion detection to investigate rubidium atoms attached to helium nanodroplets in a molecular beam experiment. The spectra of atomic Rb electronic states show a vastly enhanced sensitivity and spectral resolution when compared to conventional pump-probe wave packet interferometry. Furthermore, the formation of Rb*He exciplex molecules is probed and for the first time a fully resolved vibrational spectrum for transitions between the lowest excited 5Π3/2 and the high-lying electronic states 2(2)Π, 4(2)Δ, 6(2)Σ is obtained and compared to theory. The feasibility of applying coherent multidimensional spectroscopy to dilute cold gas phase samples is demonstrated in these experiments.